The more common term for this type of audio processing is referred to as AGC or Automatic Gain Control. A good number of camcorders have this built in already. It sounds like the issue with the youtube implementation is that the max gain allowed is just too much and the attack rate (for gaining up) is way too fast. Artistically they should allow you to turn it off or adjust the parameters, otherwise they just made all new music on the site sound bad.

Classic compression, on the other hand, is when the loud stuff is made quieter but the quiet stuff stays quiet. If you plot an input level vs output level you get a 'knee' where the threshold for compression begins. The angle of the knee is determined by the ratio of compression.

AGC is like someone has the volume knob and cranks it up so that you can always hear something regardless of the content. Usually there are minimum thresholds and max gain settings to go along with this to adjust issues such as these.

Normalizing is yet another technique which requires non-realtime analysis of the entire piece to determine and set a single gain setting for the entire file; a sort of best fit gain.

And from the more complex end, there's Dolby Volume which incorporates several of the above features with their own 'special sauce' in an attempt to provide uniform listening levels between sources and content. I haven't heard it yet to know if it is any good.

-david